Set Of Snapshots Research Articles

Analysis of unsteady wake flow in centrifugal pump volute by using mode decomposition method

To analyze the coherent structure of wake flow in volute and its corresponding frequency information, dynamic modal decomposition (DMD), classic and spectral proper orthogonal decomposition (SPOD), were employed to decompose the transient flow field of the centrifugal pump volute. The snapshot set was constructed by means of the velocity field data at different moments in volute based on the large eddy simulation (LES) approach. The basic principles of the DMD, POD, and SPOD methods were compared in detail, and the decomposition results of the three methods on the wake flow structure in volute were compared and analyzed. The analysis results show that DMD can decompose the wake flow into coherent structures with different frequencies, including the basic steady-state structure, the dynamic modal flow field structure characterizing rotor–stator interaction (the first three modes with frequencies of 145.81, 291.61, and 437.43 Hz, respectively), and dissipative modal flow field structure characterizing fragmentized vortex (the fourth mode with a frequency of 486.03 Hz) in the volute. The POD can decompose the wake flow into flow structures with different energy levels. The first four modal energies account for more than 66% of total energy, which represents the large-scale structure with higher energy, and its dominant frequencies correspond to the blade passing frequency (145 Hz) and its frequency multiplication (290 Hz). The SPOD can not only decompose the complex wake flow into structural features of different energy levels but also has single-frequency characteristics of its modal structures. Compared with DMD and POD methods, the SPOD has the advantages of both, and can reflect the evolution characteristics of the wake flow in the volute.

A Multi-Shot Approach for Spatial Resolution Improvement of Multispectral Images from an MSFA Sensor.

Multispectral imaging technology has advanced significantly in recent years, allowing single-sensor cameras with multispectral filter arrays to be used in new scene acquisition applications. Our camera, developed as part of the European CAVIAR project, uses an eight-band MSFA to produce mosaic images that can be decomposed into eight sparse images. These sparse images contain only pixels with similar spectral properties and null pixels. A demosaicing process is then applied to obtain fully defined images. However, this process faces several challenges in rendering fine details, abrupt transitions, and textured regions due to the large number of null pixels in the sparse images. Therefore, we propose a sparse image composition method to overcome these challenges by reducing the number of null pixels in the sparse images. To achieve this, we increase the number of snapshots by simultaneously introducing a spatial displacement of the sensor by one to three pixels on the horizontal and/or vertical axes. The set of snapshots acquired provides a multitude of mosaics representing the same scene with a redistribution of pixels. The sparse images from the different mosaics are added together to get new composite sparse images in which the number of null pixels is reduced. A bilinear demosaicing approach is applied to the composite sparse images to obtain fully defined images. Experimental results on images projected onto the response of our MSFA filter show that our composition method significantly improves image spatial resolution and minimizes reconstruction errors while preserving spectral fidelity.

Efficient mini-batch stochastic gradient descent with Centroidal Voronoi Tessellation for PDE-constrained optimization under uncertainty

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is frequently utilized in engineering, biology and finance. Although stochastic gradient descent is a well-known stochastic optimization technique for solving the approximate optimal control problem, it often exhibits a slow convergence rate due to the inherent variance in gradient approximation. To address this issue, we propose a more efficient stochastic optimization algorithm based on Centroidal Voronoi Tessellation sampling. This strategy reduces the error in gradient estimation compared to the conventional mini-batch stochastic gradient descent method. Our approach involves dividing the whole snapshot set into several Voronoi cells with low variance and extracting samples with good uniformity from each region to construct an unbiased estimation of the full gradient. Our method can economically and stably approximate numerical optimal control functions even with a fixed step size. Numerical results demonstrate that the proposed method is a reliable algorithm with great potential for applications in the field of optimization.

Physics-informed generator-encoder adversarial networks with latent space matching for stochastic differential equations

We propose a new class of physics-informed neural networks, called Physics-Informed Generator-Encoder Adversarial Networks, to effectively address the challenges posed by forward, inverse, and mixed problems in stochastic differential equations (SDEs). In these scenarios, while governing equations are known, the available data consist of only a limited set of snapshots for system parameters. Our model consists of two key components: the generator and the encoder, both updated alternately by gradient descent. In contrast to previous approaches that directly match approximated solutions with real snapshots, we employ an indirect matching operating within the lower-dimensional latent feature space. This method circumvents challenges associated with high-dimensional inputs and complex data distributions in solving SDEs. Numerical experiments indicate that, compared to existing deep learning solvers, our proposed approach not only demonstrates superior accuracy but also exhibits advantages in both computational efficiency and model complexity.

Stability analysis of a uniform viscous transonic flow past a rotating circular cylinder

This work analyzes the transonic flow around a rotating circular cylinder. The combination of a uniform freestream flow and the flow due to the rotation of the cylinder (assuming clockwise rotation) generates a lift force (Robins-Magnus effect) that, for transonic flows, is conditioned by the presence of a shock wave on the upper side of the cylinder.Previous studies have focused primarily on incompressible flows, compressible flows at low Mach numbers, and hypersonic flows with detached shock waves. These works have barely considered the effect of the presence of the shock wave, its interaction with the wake of the cylinder and its impact in the aerodynamic coefficients.Two-dimensional numerical simulations have been carried out using the SU2 code. From these simulations, the value of the aerodynamic coefficients as a function of time and a set of snapshots of the fluid field have been obtained and analyzed using the POD and DMD techniques. This has allowed the identification of the dominant modes that characterize the time variations in the lift and drag coefficients acting on the circular cylinder for different values of the characteristic parameters of the problem.

A lucky covariance estimator using cumulative coherence

This talk demonstrates a technique to improve covariance estimation using the principles of lucky signal processing and the cumulative coherence. Lucky processing, popularized in astro-photography, is a technique that increases signal quality by selectively keeping only a small fraction from a pool of potential snapshots. Cumulative coherence, a measure of how well a set of vectors is described by its subsets, provides the measure of “data quality” that enables the lucky processing. This approach was applied to covariance estimation on an acoustic array by taking a fixed duration sample of data and creating a dense set of snapshots with higher than usual overlap. From these densely sampled snapshots, the “luckiest” ones were found using cumulative coherence, and the covariance was averaged as normal. It was found that the lucky covariance estimate was successful at adaptive matched field processing and produced a less ambiguous processor output than the conventional estimator. The lucky covariance estimate had a higher estimated signal-to-noise ratio, especially when the source was at longer ranges from the array. [This work is supported by the Office of Naval Research.]

Direct Poisson neural networks: learning non-symplectic mechanical systems

In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid body). Mechanical systems have Hamiltonian evolution, which consists of two building blocks: a Poisson bracket and an energy functional. We feed a set of snapshots of a Hamiltonian system to our neural network models which then find both the two building blocks. In particular, the models distinguish between symplectic systems (with non-degenerate Poisson brackets) and non-symplectic systems (degenerate brackets). In contrast with earlier works, our approach does not assume any further a priori information about the dynamics except its Hamiltonianity, and it returns Poisson brackets that satisfy Jacobi identity. Finally, the models indicate whether a system of equations is Hamiltonian or not.

A lucky covariance estimator based on cumulative coherence.

The performance of adaptive acoustic localization methodologies depends on the quality of the covariance matrix being inverted. This paper demonstrates a technique to improve covariance estimation using the principles of lucky signal processing and the cumulative coherence. Lucky processing, popularized in astro-photography, is a technique that increases signal quality by selectively keeping only a small fraction from a pool of potential snapshots. Cumulative coherence, a measure of how well a set of vectors is described by its subsets, provides the measure of "data quality" that enables the lucky processing. This approach was applied to covariance estimation on an acoustic array by taking a fixed duration sample of data and creating a dense set of snapshots with higher than usual overlap. From these densely sampled snapshots, the "luckiest" ones were found using cumulative coherence, and the covariance was averaged as normal. Using data from the SWellEX-96 experiment, this new estimator was compared with standard practice. It was found that the lucky covariance estimate was successful at adaptive matched field processing and produced a less ambiguous processor output than the conventional estimator. The lucky covariance estimate had a higher estimated signal-to-noise ratio, especially when the source was at longer ranges from the array.

South African Silences, Japanese Erasures: Blackman Ngoro and the Persistence of Apartheid

This article is a “forensic inductive” reflection on the silences and erasures, in South Africa and Japan, that mark the last years of Zimbabwean journalist, Roderick Blackman Ngoro. Ngoro was ostracised in South Africa after he penned a controversial blog article about “Coloureds”. After the affair, Ngoro relocated to Japan, continuing his journalistic research on racism. He returned quietly to South Africa a few years later to pursue doctoral studies at Wits University. In late January 2010, Ngoro was found dead in his room at the university. Police did not suspect any foul play. I deploy a purposive set of snapshots as part of a reflection on how Ngoro’s last few years in South Africa and Japan illustrate the persistence of apartheid. I consider the problem of undetectable crimes scenes by means of specific inductive forensics of snapshots that allow a demonstration of how, at the crime scenes of apartheid, no foul play is detectable. Forensic induction is a methodology drawn from my emerging work in Apartheid Studies, seeking to explain how the worlds of the oppressed are crime scenes in which people live with harm and live in harm’s way. I conclude that the complex ironies that attended Ngoro’s last few years cannot make sense if not looked at through the lens of apartheid as a paradigm and theoretical framework (by which to detect persistent crime scenes). Such a paradigm has utility in detecting the persistence of harm from South Africa to Japan.

Urban Traffic Flow Congestion Prediction Based on a Data-Driven Model

Intelligent transportation systems need to realize accurate traffic congestion prediction. The spatio-temporal features of traffic flow are essential to analyze and predict congestion. Our study proposes a data-driven model to predict the traffic congested flow. Firstly, the traffic zone/grid method is used to store the local area roads’ average speed of the vehicles. Second, the discrete snapshot set is proposed to characterize traffic flow’s spatial and temporal features over a continuous period. Third, the evolution of traffic congested flow in various time dimensions (weekly days, weekend days, and one week) is examined by transforming the global urban transportation network into traffic zones. Finally, the data-driven model is constructed to predict urban road traffic congestion by using the extracted spatio-temporal characteristics of traffic zones’ traffic flow, the snapshot set of which serves as inputs for this model. The model adopts the convolutional LSTM network to learn the temporal and local spatial features of traffic flow, while utilizing a convolutional neural network to effectively capture the global spatial features inherent in traffic flow. The numerical experiments are conducted on two cities’ transportation networks, and the results demonstrate that the performance of the proposed model outperforms traditional traffic flow prediction models.

POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution: Error bounds for the pressure

Abstract Reduced order methods (ROMs) for the incompressible Navier–Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed finite element method (FOM). In addition, the set of snapshots contains the mean velocity of the FOM. Both the FOM and the POD-ROM are equipped with a grad-div stabilization. A velocity error analysis for this method can be found already in the literature. The present paper studies two different procedures to compute approximations to the pressure and proves error bounds for the pressure that are independent of inverse powers of the viscosity. Numerical studies support the analytic results and compare both methods.

POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier–Stokes equations by means of proper orthogonal decomposition (POD) methods. Our set of snapshots includes the velocity approximation at the initial time from a full order mixed finite element method (FOM) together with approximations to the time derivative at different times. The approximation at the initial velocity can be replaced by the mean value of the velocities at the different times so that when implementing the method to the fluctuations, as done mostly in practice, only approximations to the time derivatives are included in the set of snapshots. For the POD method we study the differences between projecting onto and . In both cases pointwise in time error bounds can be proved. Including grad-div stabilization in both the FOM and the POD methods, error bounds with constants independent of inverse powers of the viscosity can be obtained.

Multi-Fidelity Uncertainty Propagation Approach for Multi-Dimensional Correlated Flow Field Responses

ABSTRACT To quantify uncertainties in the multidimensional correlated flow field responses resulting from uncertain model parameters in computational fluid dynamics (CFD), this paper proposes an uncertainty quantification framework that utilises proper orthogonal decomposition (POD) and a co-Kriging model. A mixed sample snapshot set containing both high- and low-fidelity responses is first formed by transferring high-fidelity responses into the space of low-fidelity responses. The use of POD on this snapshot set reduces the multidimensional correlated responses to reduced-dimension responses, which are coefficients of basis functions. A co-Kriging model is then established between the input parameters and reduced-dimension responses. This comprehensive model enables predictions of multidimensional correlated responses under new input parameters. Through an analysis of a NACA0012 airfoil, it is demonstrated that the proposed multi-fidelity approach offers significant advancements in accuracy and efficiency compared to the single-fidelity model, providing an efficient prediction model for uncertainty propagation analysis.

Reduced-order modeling for stochastic large-scale and time-dependent flow problems using deep spatial and temporal convolutional autoencoders

A non-intrusive reduced-order model based on convolutional autoencoders is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatiotemporal large-scale flow problems. The objective is to perform accurate and rapid uncertainty analyses of the flow outputs of interest for which the input parameters are deemed uncertain. The data are constituted from a set of high-fidelity snapshots, collected using an inhouse high-fidelity flow solver, which correspond to a sample of the uncertain input parameters. The method uses a 1D-convolutional autoencoder to reduce the spatial dimension of the unstructured meshes used by the flow solver. Another convolutional autoencoder is used for the time compression. The encoded latent vectors, generated from the two compression levels, are then mapped to the input parameters using a regression-based multilayer perceptron. The proposed model allows for rapid predictions for unseen parameter values, allowing the output statistical moments to be computed efficiently. The accuracy of the proposed approach is compared to that of the linear reduced-order technique based on an artificial neural network through two benchmark tests (the one-dimensional Burgers and Stoker’s solutions) and a hypothetical dam break flow problem, with an unstructured mesh and over a complex bathymetry river. The numerical results show that the proposed methods present strong predictive capabilities to accurately approximate the statistical moments of the outputs. In particular, the predicted statistical moments are oscillations-free, unlike those obtained with the traditional proper orthogonal decomposition method. The proposed reduction framework is simple to implement and can be applied to other parametric and time-dependent problems governed by partial differential equations, which are commonly encountered in many engineering and science problems.

Reduced-order modeling using the frequency-domain method for parabolic partial differential equations

<abstract><p>This paper suggests reduced-order modeling using the Galerkin proper orthogonal decomposition (POD) to find approximate solutions for parabolic partial differential equations. We first transform a parabolic partial differential equation to the frequency-dependent elliptic equations using the Fourier integral transform in time. Such a frequency-domain method enables efficiently implementing a parallel computation to approximate the solutions because the frequency-variable elliptic equations have independent frequencies. Then, we introduce reduced-order modeling to determine approximate solutions of the frequency-variable elliptic equations quickly. A set of snapshots consists of the finite element solutions of the frequency-variable elliptic equations with some selected frequencies. The solutions are approximated using the general basis of the high-dimensional finite element space in a Hilbert space. reduced-order modeling employs the Galerkin POD for the snapshot subspace spanned by a set of snapshots. An orthonormal basis for the snapshot space can be easily computed using the spectral decomposition of the correlation matrix of the snapshots. Additionally, using an appropriate low-order basis of the snapshot space allows approximating the solutions of the frequency-variable elliptic equations quickly, where the approximate solutions are used for the inverse Fourier transforms to determine the approximated solutions in the time variable. Several numerical tests based on the finite element method are presented to asses the efficient performances of the suggested approaches.</p></abstract>

Active-learning-based nonintrusive model order reduction

Abstract Model order reduction (MOR) can provide low-dimensional numerical models for fast simulation. Unlike intrusive methods, nonintrusive methods are attractive because they can be applied even without access to full order models (FOMs). Since nonintrusive MOR methods strongly rely on snapshots of the FOMs, constructing good snapshot sets becomes crucial. In this work, we propose a novel active-learning-based approach for use in conjunction with nonintrusive MOR methods. It is based on two crucial novelties. First, our approach uses joint space sampling to prepare a data pool of the training data. The training data are selected from the data pool using a greedy strategy supported by an error estimator based on Gaussian process regression. Second, we introduce a case-independent validation strategy based on probably approximately correct learning. While the methods proposed here can be applied to different MOR methods, we test them here with artificial neural networks and operator inference.

Augmented reduced order models for turbulence

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L2-, H1- and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.

A new method for transformer hot-spot temperature prediction based on dynamic mode decomposition

The Accurate prediction of a hot spot temperature (HST) is critical for ensuring the reliable operation of transformers. The existing HST prediction methods are based on the black-box model. They cannot take into account both the real-time prediction and the acquisition of the winding temperature field, and the prediction results are unexplained. Therefore, a new HST prediction method based on dynamic mode decomposition (DMD) is proposed in this study. First, the electromagnetic-thermal-flow coupling model of a transformer winding temperature field was established for a transient calculation. A simulation snapshot set of the winding temperature field was obtained. DMD and DMD dominant modes selection were then performed on the snapshot set. Finally, the HST and winding temperature field distributions at the subsequent times were predicted by the DMD dominant modes and their revolution laws. By comparing the prediction results of the HST and winding temperature field distribution with the simulation and experimental measurement results, the speed and accuracy of the proposed prediction method were verified. The DMD-based prediction method can predict the HST and winding temperature field distribution in a few seconds and has a clear physical meaning. • Transformer model for analysing electromagnetic-thermal-flow coupling is proposed. • Prediction method based on dynamic mode decomposition is proposed. • Hot-spot temperatures and winding temperature fields of transformers are predicted. • An experimental platform is built to verify the validation of the proposed method.

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification.

Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A variety of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behaviour in time. The majority of DMD algorithms, however, are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities. Here, the optimized DMD algorithm is improved by using statistical bagging methods whereby a single set of snapshots is used to produce an ensemble of optimized DMD models. The outputs of these models are averaged to produce a bagging, optimized dynamic mode decomposition (BOP-DMD). BOP-DMD improves performance by stabilizing and cross-validating the DMD model by ensembling; it also robustifies the model and provides both spatial and temporal uncertainty quantification (UQ). Thus, unlike currently available DMD algorithms, BOP-DMD provides a stable and robust model for probabilistic, or Bayesian, forecasting with comprehensive UQ metrics. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

Learning a Weather Dictionary of Atmospheric Patterns Using Latent Dirichlet Allocation

AbstractMid‐latitude circulation dynamics is often described in terms of weather regimes. Each pattern is given by a given combination of several synoptic objects (cyclones and anticyclones). Such intrication makes it arduous to quantify recurrence and intensity of climate extremes. Here we apply Latent Dirichlet Allocation (LDA), used for topic modeling in linguistics, to build a weather dictionary: we define daily maps of a gridded target observable as documents, and the grid‐points composing the map as words. LDA provides a representation of documents in terms of a combination of spatial patterns named motifs, which are latent patterns inferred from the set of snapshots. For atmospheric data, we find that motifs correspond to pure synoptic objects (cyclones and anticyclones), that can be seen as building blocks of weather regimes. We show that LDA weights provide a natural way to characterize the impact of climate change on the recurrence of patterns associated with extreme events.